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Order asymptotically isometric copies of co in the subspaces of order continuous elements in Orlicz spaces

2014
journal article
article
Journal
Journal of Convex Analysis
Author
Cui Yunan

Hudzik Henryk

Lewicki Grzegorz
Volume
21
Number
3
Pages
663-680
ISSN
0944-6532
eISSN
2363-6394
Language
English
Journal language
English
Abstract in English

Necessary and sufficient conditions in order that the subspace of order continuous elements of Orlicz sequence space contain an order asymptotically isometric copy of are given for both, the Luxemburg and the Amemiya-Orlicz norm. In case of a non-atomic, complete and finite measure space and the Luxemburg norm (the Amemiya-Orlicz norm) such criteria are obtained under the additional assumption that the space is a dual space (resp. the space is a dual and non-square space). In both cases, the Luxemburg and the Amemiya-Orlicz norm the criteria are given under the necessary assumption that the spaces and are non-trivial. The asymptotically isometric copies of that are built in our theorems are order copies.

Affiliation
Wydział Matematyki i Informatyki : Instytut Matematyki
dc.abstract.enNecessary and sufficient conditions in order that the subspace of order continuous elements of Orlicz sequence space contain an order asymptotically isometric copy of $c_0$ are given for both, the Luxemburg and the Amemiya-Orlicz norm. In case of a non-atomic, complete and $\sigma-$finite measure space $(T,\Sigma,\mu)$ and the Luxemburg norm (the Amemiya-Orlicz norm) such criteria are obtained under the additional assumption that the space $L^\Phi(T,\Sigma,\mu)$ is a dual space (resp. the space $L^\Phi_A(T,\Sigma,\mu)$ is a dual and non-square space). In both cases, the Luxemburg and the Amemiya-Orlicz norm the criteria are given under the necessary assumption that the spaces $E^\Phi(T,\Sigma,\mu)$ and $E^\Phi_A(T,\Sigma,\mu)$ are non-trivial. The asymptotically isometric copies of $c_0$ that are built in our theorems are order copies.pl
dc.affiliationWydział Matematyki i Informatyki : Instytut Matematykipl
dc.contributor.authorCui, Yunanpl
dc.contributor.authorHudzik, Henrykpl
dc.contributor.authorLewicki, Grzegorz - 129946 pl
dc.date.accessioned2015-03-06T09:22:16Z
dc.date.available2015-03-06T09:22:16Z
dc.date.issued2014pl
dc.description.number3pl
dc.description.physical663-680pl
dc.description.volume21pl
dc.identifier.eissn2363-6394pl
dc.identifier.issn0944-6532pl
dc.identifier.urihttp://ruj.uj.edu.pl/xmlui/handle/item/3583
dc.languageengpl
dc.language.containerengpl
dc.rights.licenceBez licencji otwartego dostępu
dc.subtypeArticlepl
dc.titleOrder asymptotically isometric copies of co in the subspaces of order continuous elements in Orlicz spacespl
dc.title.journalJournal of Convex Analysispl
dc.typeJournalArticlepl
dspace.entity.typePublication
dc.abstract.enpl
Necessary and sufficient conditions in order that the subspace of order continuous elements of Orlicz sequence space contain an order asymptotically isometric copy of $c_0$ are given for both, the Luxemburg and the Amemiya-Orlicz norm. In case of a non-atomic, complete and $\sigma-$finite measure space $(T,\Sigma,\mu)$ and the Luxemburg norm (the Amemiya-Orlicz norm) such criteria are obtained under the additional assumption that the space $L^\Phi(T,\Sigma,\mu)$ is a dual space (resp. the space $L^\Phi_A(T,\Sigma,\mu)$ is a dual and non-square space). In both cases, the Luxemburg and the Amemiya-Orlicz norm the criteria are given under the necessary assumption that the spaces $E^\Phi(T,\Sigma,\mu)$ and $E^\Phi_A(T,\Sigma,\mu)$ are non-trivial. The asymptotically isometric copies of $c_0$ that are built in our theorems are order copies.
dc.affiliationpl
Wydział Matematyki i Informatyki : Instytut Matematyki
dc.contributor.authorpl
Cui, Yunan
dc.contributor.authorpl
Hudzik, Henryk
dc.contributor.authorpl
Lewicki, Grzegorz - 129946
dc.date.accessioned
2015-03-06T09:22:16Z
dc.date.available
2015-03-06T09:22:16Z
dc.date.issuedpl
2014
dc.description.numberpl
3
dc.description.physicalpl
663-680
dc.description.volumepl
21
dc.identifier.eissnpl
2363-6394
dc.identifier.issnpl
0944-6532
dc.identifier.uri
http://ruj.uj.edu.pl/xmlui/handle/item/3583
dc.languagepl
eng
dc.language.containerpl
eng
dc.rights.licence
Bez licencji otwartego dostępu
dc.subtypepl
Article
dc.titlepl
Order asymptotically isometric copies of co in the subspaces of order continuous elements in Orlicz spaces
dc.title.journalpl
Journal of Convex Analysis
dc.typepl
JournalArticle
dspace.entity.type
Publication
Affiliations
Wydział Matematyki i Informatyki
Lewicki, Grzegorz
No affiliation
Cui, Yunan
Hudzik, Henryk

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